SHOW CALCULATIONS TO GET FULL CREDIT        1. The personnel director of a large corporation wants to study absenteeism among      clerical workers at the corporation’s central office during the year. A random      sample of 25 clerical workers reveals the following: [20 points]   Absenteeism: = 19.7 days, S = 5.0 days.                    20 clerical workers were absent more than 12 days.   Set up an 95 % confidence interval estimate of the average number of absences for clerical workers last year.   Set up a 90% confidence interval estimate of the population proportion of clerical workers absent more than 12 days last year.   If the personnel director also wants to take a survey in a branch office, what sample size is needed if the director wants to be 95% confident of being correct to within ± 1.5 days and the population standard deviation is assumed to be 4.5 days?   If the personnel director also wants to take a survey in a branch office, what sample size is needed if the director wants to be 99% confident of being correct to within ± 0.035 of the population proportion of workers who are absent more than 12 days if the population proportion is known to be 0.45.